Well other than the foreigners employed at international schools that require at a bare minimum a teaching license +Bed and relevant teaching experience in the home country, I'd say that the percentage of teachers teaching content is quite low. Even the few guys I know at universities sometimes get thrown a bone and can dabble a bit in English lit (they have the appropriate graduate degrees to do so), but they will never be able to shake the EFL "communication skills" courses.

I don't count test prep because a lot of it falls within EFL (TOEIC etc..).

Basically if a Korean can do it, there is no reason why a waegukin would be employed for a position that requires content teaching. The way I see it, you're hired for your native speaker intuition and that is basically it. Anything other teaching position a Korean national can do. If Koreans suddenly were learning English from their own teachers like they do in Finland I don't think it is a stretch of the imagination to say that the E2 would cease to exist for NETs.

Well other than the foreigners employed at international schools that require at a bare minimum a teaching license +Bed and relevant teaching experience in the home country, I'd say that the percentage of teachers teaching content is quite low. Even the few guys I know at universities sometimes get thrown a bone and can dabble a bit in English lit (they have the appropriate graduate degrees to do so), but they will never be able to shake the EFL "communication skills" courses.

I don't count test prep because a lot of it falls within EFL (TOEIC etc..).

Basically if a Korean can do it, there is no reason why a waegukin would be employed for a position that requires content teaching. The way I see it, you're hired for your native speaker intuition and that is basically it. Anything other teaching position a Korean national can do. If Koreans suddenly were learning English from their own teachers like they do in Finland I don't think it is a stretch of the imagination to say that the E2 would cease to exist for NETs.

I started off in Seoul working in the SMOE program but now I teach Social Studies at an international school here. My undergrad major was History and I do have a teaching credential from the US in Social Studies so it's been a great transition.

An English/UK man teaching philosophy.
A Canadian teaching physics with a nuclear bent (I think).

Elsewhere....
I know one woman years ago taught something drama related.
American teaching some sort of business with an MBA course up in Seoul.
A Elementary school teacher at a US military school.

This is just off the top of my head.

Fair enough, but I would argue that KAIST doesn't exactly represent higher education in Korea as a whole. It is the elite of the elite in the ROK so they will have foreign professors. Those professors will be actual professors with a publication track record and a doctorate to go along with it I would think. They didn't come to the ROK to teach EFL like the majority of us here did.
Seeing that this is an EFL board I think the OP was reaching out to us fellow NETs wondering if any of us was eventually able to get into teaching anything BUT conversational English. I would think that a doctorate holder with a distinguished publication record at home that came to Korean university to lecture and do research in their academic field wouldn't be on ESL cafe.

Do some NETs eventually shake the yoke of EFL and get into teaching something they did their BA and MA in? Maybe but I don't think it is very common. The opportunities are just too few and far between and like I said before, a Korean academic will do it unless it is a prestigious university like KAIST that actively seeks foreign professors from abroad directly.

Do all international schools require a teaching certificate / degree or is a graduate degree sometimes enough? I often kick myself for not going the teacher's certificate route.

The real ones do. And by real ones I mean the ones that will pay you an equivalent salary and benefits (maybe more) that you will get at home if you were a tenured public school teacher.

Legitimate international schools will require at a minimum a B'Ed + teaching experience/license in the home country.

There are many schools in Korea that call themselves "international schools" for marketing purposes or maybe because they offer some content based English classes for kids. These schools will pay just like any other hagwon or PS school will pay for a NET based on what I know.I'm sure some of the more seasoned posters here could chime in on this as they know much more than me.

Do all international schools require a teaching certificate / degree or is a graduate degree sometimes enough? I often kick myself for not going the teacher's certificate route.

Those that are internationally accredited (by the likes of IBO and others) REQUIRE (as part of their accreditation) that their teachers be properly certified teachers with certain defined minimums of experience. Their remuneration packages are certainly attractive enough to get the level of teachers they want and require.

They may make exceptions in things like specialized science courses or higher level mathematics (want to teach AP Physics or Integral Calculus classes?)

Those schools that are "international" in name only will probably take someone with graduate level credentials even though they are not certified teachers.

Graduate level credentials will usually be enough to get into university positions at a minimum of "guest lecturer" and often as "visiting professor" in many countries in Asia including Korea, China, Thailand and Malaysia.

I know a ton of foreigners who teach content at the high school and college level -- economics, history, design, etc.

Thing is, to do so you have to: 1) be really good at what you do, and/or 2) have an F-series visa, which makes you less of a hiring headache, and/or 3) have the connections to these gigs or put in your time to work up to them.

I also teach SAT, a heck of a lot of English lit, and a growing amount of college pre-reading. Test prep certainly ain't ESL, and especially not if you're considering the SAT II/AP math, science, history, etc tests.

Can foreigners do courses that more in line with their majors? Sure! You need to realize that you're at a serious disadvantage as you're an outsider lecturing in a foreign language, so your game will have to be good enough to make up for that fact. And like I said, it may take a while for you to build up your reputation/connections. But I can tell from looking at my buds that decent gigs are out there for talented, professional folks... don't lose heart; keep looking.

Questions for the people teaching in Int schools here: how stiff was the competition? Did you already have teaching experience in your own country? A masters degree? Did the name recognition of your degree matter? Were you recruited through ISS or international school fairs overseas or locally? Do the pay and benefits make up for the extra paperwork and responsibilities involved? Are there any spoiled brats in your classes who don't give a toss?